Two different analytical tests can be used to determine the impurity level in steel alloys. Nine specimens are tested using both procedures, and the results are shown in the tabulation.Find the 95\% confidence interval for the mean difference of the tests, and explain it.

UkusakazaL 2021-07-31 Answered

Two different analytical tests can be used to determine the impurity level in steel alloys. Nine specimens are tested using both procedures, and the results are shown in the following tabulation.
SpecimenTest1Test211.21.421.61.731.51.541.41.351.82.061.82.171.41.781.51.691.41.5
Find the 95% confidence interval for the mean difference of the tests, and explain it.

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Cheyanne Leigh
Answered 2021-08-03 Author has 1 answers

Step 1
Test1(X)Test2(Y)(xx¯)(xx¯)2(yy¯)(ybary)21.21.40.311110.096790.244440.059751.61.70.088890.007900.055560.003091.51.50.011110.000120.144440.020861.41.30.111110.012350.344440.118641.82.00.288890.083460.355560.126421.82.10.288890.083460.455560.207531.41.70.111110.012350.055560.003091.51.60.011110.000120.044440.001981.41.50.111110.012350.144440.02086
Step 2
The mean is given by
x=1nx
Test 1 NKS x=13.69=1.511
Test 2
y=14.89=1.644
The standard deviation is given by
σ=1n1(xx)2
Test 1
σ=0.308898=0.1965
Test 2
s2=0.56228=0.2651
The 95% CI is given by
C.I.=(xy)±t0.05, 8s12n1+s22n2
C.I.=(1.5111.644)±2.306(0.1965)29+(0.2651)29
C.I.=[0.387, 0.120]
It shows that the true difference between the mean of test 1 and test 2 will lie within -0.387 and 0.120.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-08-03
A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is σ=15
a) Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.
b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places.
c) What is the effect of a larger sample size on the interval estimate?
Larger sample provides a-Select your answer-largersmallerItem 5 margin of error.
asked 2021-08-09

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 13 subjects had a mean wake time of 101.0 min. After​ treatment, the 13 subjects had a mean wake time of 94.6 min and a standard deviation of 24.9 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
Construct the 95% confidence interval estimate of the mean wake time for a population with the treatment.
min<μ<min ​(Round to one decimal place as​ needed.)
What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
The confidence interval ▼ does not include| includes the mean wake time of 101.0 min before the​ treatment, so the means before and after the treatment ▼ could be the same |are different. This result suggests that the drug treatment ▼ does not have | has a significant effect.

asked 2021-02-23
Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let j: denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence intervals (7-8, 9.6)
(a) Would 2 90%% confidence interval calculated from this same sample have been narrower or wider than the glven interval? Explain your reasoning.
(b) Consider the following statement: There is 9 95% chance that Is between 7.8 and 9.6. Is this statement correct? Why or why not?
(c) Consider the following statement: We can be highly confident that 95% of al bottles ofthis type of cough syrup have an alcohol content that is between 7.8 and 9.6. Is this statement correct? Why or why not?
asked 2021-08-12

In a science fair​ project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left​ hand, and then she asked the therapists to identify the selected hand by placing their hand just under​ Emily's hand without seeing it and without touching it. Among 358 ​trials, the touch therapists were correct 172 times. Complete parts​ (a) through​ (d).
a) Given that Emily used a coin toss to select either her right hand or her left​ hand, what proportion of correct responses would be expected if the touch therapists made random​ guesses? ​(Type an integer or a decimal. Do not​ round.)
b) Using​ Emily's sample​ results, what is the best point estimate of the​ therapists' success​ rate? ​(Round to three decimal places as​ needed.)
c) Using​ Emily's sample​ results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.
Round to three decimal places as​ needed - ?<p<?

asked 2020-10-28
Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50)
Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50)
What is Jo’s margin of error, rounded to the nearest whole number?
asked 2020-10-18
Consider the following function. f(x)=x2x281 a) To find the critucal numbers of f. b) To find the open interval on which function is increasing or decreasing. c) To identify the relative extremum.
asked 2022-04-22
How can I find the Margin of Error E
The professor hasn't gone over this section but I want to understand it so that I won't confused in class. I want to learn so that I can do the other problems.
So this is the problem, If anyone could teach me so I could take note I'd deeply appreciate it. Thank you for your time.
Question: Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. n=550, x equals 330, 90 % confidence
I know how to obtain the alpha/2 to find the confidence.
I just went over the Binomial Distribution and Limit Theorem, which understand now this is next. If anyone would care to spent their time explaining I'd be forever grateful, thank you again for your time.